1. Field of the Invention
The present invention relates to a method for extracting formant frequencies from vowels or voiced consonants of a speech sound.
2. Description of the Prior Art
It is known that the formant frequency is one of the important characteristics of speech sounds such as vowels and voiced consonants. Specifically in the case of identifying a vowel, it is known that it is generally sufficient if a first formant frequency (F1) and a second formant frequency (F2) are known. In order to achieve the extraction of such two formant frequencies using an inexpensive system such as an 8-bit personal computer, a high speed formant extraction method is desired.
FIG. 7 is a processing flow chart in a prior art formant extraction method. In a voice signal input step 11, the voice is stored in a RAM through a microphone and an A/D converter. In a linear prediction coefficient calculation step 12, a p-th degree of linear prediction coefficients for one frame length, for example, of 20 ms is calculated. An inverse filter using linear prediction coefficients is given by ##EQU1## where a.sub.1, a.sub.2, . . . , a.sub.p are linear prediction coefficients. A root solving step 40 solves all roots of the filter of an all-zero type by the Newton-Raphson method. The frequency F and the bandwidth B corresponding to a root z.sub.i are obtained by EQU F=(f.sub.s /2.pi.) tan.sup.-1 [I.sub.m (z.sub.i)/R.sub.e (z.sub.i)] (Hz) (1) EQU B=(f.sub.s /.pi.) ln (z.sub.i) (2)
where f.sub.s is the sampling frequency. In a postprocessing step 41, from all the roots obtained in the root solving step 40, roots whose bandwidths B are less than a threshold value or which have continuity in frequency from and to the results in the preceding and following frames are selected, and the lowest frequency root is determined to be the first formant frequency and the next lowest is determined to be the second formant frequency.
In such a method, however, it takes a considerable length of time to obtain the roots, about which an explanation will be given with reference to FIG. 8. FIG. 8 is a flow chart of the operations of the root solving step 40. In step 70, a constant z.sub.0 is substituted for Z.sub.i as an initial value of a root candidate. In step 71, A(z.sub.i) and A'(z.sub.i), the linear differential of A(z.sub.i) are calculated. At step 72, a determination is made as to whether or not the absolute value of A(z.sub.i)/A'(z.sub.i), i.e., the difference between the values after renewal and before renewal of Z.sub.i is smaller than a threshold value. If the absolute value is not smaller than the threshold value, z.sub.i is renewed in step 73 and goes back to step 71. But, if the absolute value is smaller than the threshold value, z.sub.i is judged to have converged to a correct root value and is determined to be a root in step 74. Then, in step 75, A(z) is divided by a quadratic expression of z.sub.i and its conjugate complex number z.sub.i *, (z-z.sub.i).multidot.(z-z.sub.i *), whereby A(z) is renewed. In step 76, a determination is made as to whether or not A(z) has become zero-order, and if it not, the flow returns to step 70 where the calculation to substitute z.sub.0 for z.sub.i is performed again. If A(z) is zero-order, the formant frequency and bandwidth are obtained for all roots using the aforementioned equations (1) and (2) in step 77 and the calculation is ended.
In the above described method, since an approximate value of the root is not known at the start, all of the roots are obtained with the same initial value. Hence, the loop from step 76 to step 70 is traversed p/2 times. In order to keep high accuracy even when the desired root is therefore obtained at the later looping, each of the roots obtained must be of high accuracy. Therefore, the threshold value must be made small enough and as a result, the loop 72.fwdarw.73.fwdarw.71 has to be traversed many times. Thus, if such a high volume of calculations is to be performed by an 8-bit personal computer, there arises a difficulty in that the processing time becomes very great and therefore such method is impractical.